@Ali Hassani  Just replace  diff  with  u(x,t)  in the code.

@nm  It's easy to fix. But OP wrote  "I want all terms with 'diff' to be moved to the left side of the equation and all source terms to be moved to the right side of the equation."

Corrections in the last lines of your code:

Reff := s -> b*1/c*eval(S(t),F(s))*1/n;
Reff(100);
plot(Reff, 0..400, 0..2.1*10^(-6)); 

@C_R  OK. Thumb up.

@CaptNnFalcon  Cylindrical coordinates  x=r*cos(phi), y=r*sin(phi), z=z :

algsubs(x^2+y^2=r^2, Eq);
map(sqrt, %) assuming positive;
solve(%, z);
2*int(r,[z=0..%[1],r=2..6, phi=0..2*Pi]);

See the new answer to your previous question  https://mapleprimes.com/questions/238052-Condition-On-The-Colors-To-Illustrate#answer301034

Thank you all very much for your helpful answers!

@mmcdara  Thank you. I'm using Maple 2018 and don't have newer versions.

@dharr  Thanks for this. I've converted your comment into an answer. In essence, this is a ready-made help page for using prefix notation. In fact, this notation is very convenient and is widely used (in particular in programming), for example when the number of operands is large or a priori unknown.

@sand15  Of course your version is simpler. Thank you.

@nm  Yes, your approach is more consistent with the wishes of the OP. In this regard, we can introduce the concept of a sublist of a given list, that is, will the list  N  be a sublist of the list  L ?

@randomuser24  Specifications of a function  f(x):= ...  or   f:=x-> ...  are equivalent in recent versions of Maple.
Examples:

 f(x):=2*x^2-4*x:
plot([f(x), 2*f(x), 4*f(x), -f(x), -2*f(x), -4*f(x)], x=-1..3, color=[red,blue,green,cyan,khaki,brown]);

f:=x->2*x^2-4*x:
plot([f(x), 2*f(x), 4*f(x), -f(x), -2*f(x), -4*f(x)], x=-1..3, color=[red,blue,green,cyan,khaki,brown]);

Don't forget to put multiplication signs where necessary; they are often missed in your text.

@C_R Yes, this is possible in Maple 2018 as well. Thank you very much.

@acer  and @ Axel Vogt  Thank you very much! 

@JAMET  Look carefully at my answer about this (multiplying a matrix by a vector).